Just to clarify: this isn't actually one of my games. It's this week's "みんなで何切る?" From MFCs website. They have a weekly problem and get a pro to comment on it after a week. My plan is to try and translate the pro commentary once it's out (next Monday).
Having said that here's my discard choice:
I felt it gave the most possibilities for developing the hand in different ways. Tanyao is pretty much guaranteed. Possible other yaku: ipeikou/double runs, Pinfu/peace. Also possible is ryanpeikou using the

.
The pairs of

and

can be developed into ipeikou or triples depending what you draw, or even drop the

and use the

as your head of you draw tiles to complete you groups in bams and craks.
The reason I leave the craks alone is that you have all tiles from

to

improving your hand in some way. The way I view it currently is three possible groups. The obvious ones are the

ipeikou and the

run. Drawing a

gets you the extra yaku and sets you up with a two way wait for Pinfu (albeit with a 6 tile wait instead of the ideal 8 ). Drawing a

allows you to get 345 and the either 666 and drop the 7 later or 66 and 67 giving you a head and a two sided wait for Pinfu. A

gives you the option of two triples 444 and 666 or a 44 456 66 and a double pair wait. Not ideal since you give up both the possibility of Pinfu and San Ankou, but in last place you need to take what you can get sometimes so if the draw gets you to tenpai with this shape then might as well take it. The

I've mentioned and is the ideal draw in craks.

allows for a 44 567 666 set up. A

gives 44 666 77 marginally better than the double pair wait above, but mostly for the extra fu. While the

is the second most ideal draw in craks as it still allows you to get ipeikou albeit at the loss of Pinfu most likely.
The bams are the least interesting in this hand. Hence the choice to drop the 3. The two sided wait to complete the run is best, and it's quite possible that you'll drop the 3 and 4 any ways to make way for extra yaku in the other suits.